Advertisement

Understanding and Mathematics

  • Francis J. Murray
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 12)

Abstract

We will now consider a general framework for “understanding.” As individuals we deal with an environment that affects us either favorably or unfavorably, and our continued existence depends on our interaction with it. Experience is this process of dealing with the environment. Experience is certainly continuous, but we consider that we can resolve it into unit sub-procedures in which we deal with a “situation” and use our understanding to guide our actions to produce a favorable result. Clearly this understanding is based on past experience or on learning, which corresponds to the experience of others. Preceding experience must, therefore, be structured into patterns that we can recognize in the situation we are dealing with.

Keywords

Exact Science Experience Pattern Comprehension Concept Conceptual Experience Conceptual Analog 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Church, Alonzo, Introduction to Mathematical Logic, Princeton University Press, Princeton, New Jersey (1956).Google Scholar
  2. 2.
    De Wulf, Maurice, The System of Thomas Aquinas (reprint), Dover Publications, Inc., New York (1959).Google Scholar
  3. 3.
    Heath, T. L., The Thirteen Books of Euclid’s Elements (reprint), Dover Publications, Inc., New York (1956).Google Scholar
  4. 4.
    Joad, C. E. M., Guide to Philosophy (reprint), Dover Publications, Inc., New York (1957).Google Scholar
  5. 5.
    Landau, Edmund, Foundations of Analysis (English translation by F. Steinhardt), Chelsea Publishing Company, New York (1951).Google Scholar
  6. 6.
    Morrow, G. R., Proclus: A Commentary on the First Book of Euclid’s Elements, Princeton University Press, Princeton, New Jersey (1970).Google Scholar
  7. 7.
    Russell, Bertrand, in: The Growth of Mathematics (Robert W. Mark, ed.), Bantam Books, New York (1964).Google Scholar
  8. 8.
    Styazhkin, N. I., History of Mathematical Logic from Leibnitz to Peano, The M.I.T. Press, Cambridge, Massachusetts (1969).Google Scholar
  9. 9.
    Takeuti, G., and Zaring, W. M., Introduction to Axiomatic Set Theory, Springer-Verlag, New York (1971).Google Scholar
  10. 10.
    Whitehead, A. N., and Russell, B., Principia Mathematica, Cambridge University Press, Cambridge, England (2nd Edition, 1929; paperback partial reprint, 1962).Google Scholar

Copyright information

© Plenum Press, New York 1978

Authors and Affiliations

  • Francis J. Murray
    • 1
  1. 1.Duke UniversityDurhamUSA

Personalised recommendations